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Deutsche Forschungsgemeinschaft

Abstract

Mass transport properties of molten iron and iron alloys at high pressures (P) and temperatures (T) are important for understanding large-scale geochemical processes related to the thermochemical evolution of planetary cores. In particular, the diffusivities of light and siderophile elements in liquid iron under the extreme P-T conditions of the Earth’s core and its formation place important kinetic constraints on the time and length scales of (1) chemical equilibration between metal and silicate during core formation, (2) compositional convection in the Earth’s liquid outer core, and (3) potential chemical stratification and exchange between mantle and core during cooling. In order to better understand the effects of P and T on Si, O, and Cr diffusion in liquid iron, as well as Fe self-diffusion, we have conducted both chemical diffusion-couple experiments using a multi-anvil press and theoretical calculations using first principles molecular dynamics (FP-MD). This is the first study to jointly use and compare experimental and computational results, conducted under similar conditions, to determine the effect of pressure on diffusion in liquid iron and iron alloys.
Diffusion coefficients calculated from FP-MD simulations are in excellent agreement with experimental results. Arrhenian activation terms obtained by both methods are in good agreement with previous empirical estimates and computational results and substantially smaller than previously reported experimental values derived from much smaller data sets. Our findings corroborate theoretical estimates that diffusion coefficients are scalable to homologous temperature (Tm/T, where Tm is the absolute melting temperature), yielding constant diffusivities of approximately 5 × 10-9 m2 s-1 for Si, Cr, and Fe and ~1 × 10-8 m2 s-1 for O along the entire melting curve from ambient to core pressures. Verification of a homologous temperature relation for diffusion in liquid iron implies that low-pressure diffusion data can be used with confidence to predict rates of mass transport in the Earth’s liquid outer core.
Mass transport properties are sensitive to structural properties of liquid metals and can therefore be used as ‘indicators’ of the liquid structure and mechanisms of alloying element incorporation, which are challenging to measure directly. The wide range of P-T conditions accessible by FP-MD simulations provides new insights into compression mechanisms operating in liquid iron alloys, as well as the relationship between transport and structural properties that may be used as a proxy to estimate the solubility and/or solid-liquid partition coefficients of relevant solute species. Accordingly, a second aspect of the dissertation is the investigation of structural properties of liquid iron alloys, i.e., average interatomic distances and local coordination environments, using partial radial distribution functions obtained from the FP-MD simulations.
We report a change in compression mechanism in liquid Fe0.96O0.04 at a simulation density of approximately 8 g cm-3. Below this density, compression is accommodated by a closer packing of both iron and oxygen atoms with an increase in coordination numbers from ~10 to ~13 and ~3 to ~6, respectively. This structural transformation coincides with an increase in the average Fe-O distances while average Fe-Fe distances remain essentially constant. Additionally, oxygen self-diffusion coefficients calculated from the atomic trajectories over this density range show a negligible pressure dependence, consistent with our experimental results up to 18 GPa. Above ~8 g cm-3, the liquid is essentially close-packed and compression is accommodated by a reduction of the atomic volume of both iron and oxygen. Above ~8 g cm-3, interatomic distances and diffusion rates for both species decrease monotonically with increasing density. The coordination of oxygen reaches a maximum of ~8.5 at ~9.4 g cm-3 and does not further increase upon further compression to 11.6 g cm-3, indicating a local B2 packing structure for Fe around O under conditions of the Earth’s core. The stable crystal structure of iron at inner core pressures is widely regarded to be hexagonal close-packed, which implies that the large strain energies associated with oxygen incorporation may result in its strong fractionation into the liquid outer core during inner core crystallization, as suggested by previous theoretical studies. Additionally, the liquid-liquid structural transformation reported here may be a viable explanation to the previously reported change from a negative to a positive pressure dependence of the solubility of oxygen in liquid iron.